Geometrical Quantization. ii. Dynamical Quantization

Stephen D. Bartlett, DAVID J. ROWE, Joe Repka

Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization, (ii) induced unitary representations corresponding to prequantization and (iii) irreducible unitary representations obtained in geometric quantization by choice of a polarization. These representations establish an intimate relation between coherent state theory and geometric quantization in the context of induced representations.

Mircea Puta

Norman E. Hurt

Stephen D. Bartlett, DAVID J. ROWE, Joe Repka

It is shown here and in the preceding paper (Bartlett S D, Rowe D J and Repka J 2002 J. Phys. A: Math. Gen. 35 ) that vector coherent state theory, the theory of induced representations and geometric quantization provide alternative but equivalent quantizations of an algebraic model. The relationships are useful because some constructions are simpler and more natural from one perspective than another. More importantly, each approach suggests ways of generalizing its counterparts. In this paper, we focus on the construction of quantum models for algebraic systems with intrinsic degrees of freedom. Semi-classical partial quantizations, for which only the intrinsic degrees of freedom are quantized, arise naturally out of this construction. The quantization of the SU (3) and rigid rotor models are considered as examples.

D. J. R. Lloyd-Evans

Nemoto, Ryusho

We propose a unified theoretical framework in which time is not treated as a coordinate, but as a quantized mediator of interaction between energy and in- formation. A new fundamental field, the tensor particle field Tµν = Eµν + iIµν, is introduced to unify the geometric curvature of relativity and the probabilistic structure of quantum mechanics. The interaction between its real and imaginary components generates a new fundamental force termed the temporal force, Ft, which governs the emergence of temporal evolution without the need for an explicit time dimension. Through a Lagrangian formalism, we show that both quantum un- certainty and relativistic covariance arise as asymptotic limits of the same tensor dynamics. This establishes time as a quantized particle phenomenon and provides a consistent bridge between quantum and relativistic physics.